Abstract
Recall that the outer automorphism group of a group G, denoted Out G , is the quotient group Aut G/ Inn G . If M is any group, then there exists a torsion-free, metabelian group G with trivial center such that Out G≅M . This answers a problem in the Kourovka Notebook (Mazurov, Khukhro, Unsolved problems in group theory; the Kourovka Notebook, Russian Academy of Science, Novosibirsk, 1992).
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